In this paper, we define a new type of cohomology for Hom-Leibniz superalgebras which controls deformations superalgebras. The and the associated deformation theory as developed here are also extended to equivariant context, under presence finite group actions on

In this paper we prove the Lovász Conjecture: If Hom (C2r+1,H) is k-connected, then χ(H) ≥ k + 4, where H is a finite undirected graph, C2r+1 is a cycle with 2r+1 vertices, r, k ∈ Z, r ≥ 1, k ≥ −1, and Hom (G,H) is the cell complex with the vertex set being the set of all graph homomorphisms from G to H , and cells all allowed list H-colorings of G. Our method is to compute, by means of spectra...

In this paper, we first introduce the notion of Reynolds operators on Hom-Leibniz algebras and give some constructions. Furthermore, define cohomology operators, use to study deformations operators. As applications, NS-Hom-Leibniz as underlying structure

The Hong-Ou-Mandel (HOM) effect is widely regarded as the quintessential quantum interference phenomenon in optics. In this work we examine how nonlinearity can smear statistical photon bunching in the HOM interferometer. We model both the nonlinearity and a balanced beam splitter with a single two-level system and calculate a finite probability of anti-bunching arising in this geometry. We thu...

LetHWR be the path on 3 vertices with a loop at each vertex. D. Galvin [4, 5] conjectured, and E. Cohen, W. Perkins and P. Tetali [2] proved that for any d-regular simple graph G on n vertices we have hom(G,HWR) ≤ hom(Kd+1, HWR). In this paper we give a short proof of this theorem together with the proof of a conjecture of Cohen, Perkins and Tetali [2]. Our main tool is a simple bijection betwe...

In this paper we prove the Lovász Conjecture: If Hom (C2r+1,H) is k-connected, then χ(H) ≥ k + 4, where H is a finite undirected graph, C2r+1 is a cycle with 2r+1 vertices, r, k ∈ Z, r ≥ 1, k ≥ −1, and Hom (G,H) is the cell complex with the vertex set being the set of all graph homomorphisms from G to H , and cells all allowed list H-colorings of G. Our method is to compute, by means of spectra...

Our purpose in this paper is the generalization of notions quadratic and symplectic structures to case 3-(Hom)-$\rho$-Lie algebras. We describe some properties them by expressing related lemmas theorems. Also, we introduce concept 3-pre-(Hom)-$\rho$-Lie algebras define their representation.

Abstract We prove a hom-associative version of Hilbert’s basis theorem, which includes as special cases both non-associative and the classical theorem for associative Ore extensions. Along way, we develop hom-module theory. conclude with some examples extensions are all noetherian by our theorem.

Set-theoretic solutions to the Yang-Baxter equation have been studied extensively by means of related algebraic systems such as cycle sets and braces, dynamical versions which also developed. No work focuses on set-theoretic Hom-Yang-Baxter (HYBE for short). This paper investigates HYBE associated system, called Hom-cycle sets. We characterize left non-degenerate involutive sets, establish thei...

Humanitarian operations management (HOM) defines the broad domain that deals with of crisis events and human suffering, a plethora research has contributed to this field. Over recent years, blockchain technology been signaled throughout literature as tool can support HOM result technology's enhanced features such security auditability. In bid explore application in HOM, we systematically review...